The correct option is C 3λ2
For the two waves having same amplitude, destructive interference results into minimum amplitude for the resultant wave.
⇒Aresultant=|A1−A2|
For the given zero resultant amplitude,
⇒Aresultant=|A−A|=0
It represents the case of destructive interference.
⇒Hence path difference between waves will be odd multiples of λ2 i.e Δx=λ2, 3λ2, 5λ2,..etc
In a generalised form,
⇒Δx=(2n+1)λ2
∴Δx=3λ2(for n=1)
Option (c) is correct.